Below are listed rank-two temperaments supported by the 16edo patent val, below the indicated cutoff in TE badness.

5-limit temperaments with badness below 0.1

Listed is the wedgie and the TE badness times 1000 for four temperaments with badness less than 0.1.

Rank	Wedgie	Name	Badness	Commas
1	<<14 6 -23]]	Vishnu	31.181	6115295232/6103515625
2	<<5 1 -10]]	Magic	39.163	3125/3072
3	<<1 -3 -7]]	Mavila	39.556	135/128
4	<<4 4 -3]]	Diminished	47.231	648/625

7-limit temperaments with badness below 0.06

Listed is the wedgie and the TE badness times 1000 for four temperaments with badness less than 0.06.

1	<<4 4 4 -3 -5 -2]]	Diminished	22.401	36/35 50/49
2	<<9 5 -3 -13 -30 -21]]	Valentine	31.056	126/125 1029/1024
3	<<1 -3 5 -7 5 20]]	Armodue	49.038	36/35 135/128
4	<<5 1 -7 -10 -25 -19]]	Muggles	56.206	126/125 525/512

11-limit temperaments with badness below 0.05

Listed is the wedgie and the TE badness times 1000 for 18 temperaments with badness less than 0.05.

Rank	Wedgie	Name	Badness	Commas
1	<<9 5 -3 7 -13 -30 -20 -21 -1 30]]	Valentine	16.687	121/120 126/125 176/175
2	<<4 4 4 12 -3 -5 5 -2 14 20]]	Demolished	26.574	36/35 45/44 50/49
3	<<1 -3 5 -1 -7 5 -5 20 8 -20]]	Armodue	27.211	33/32 36/35 45/44
4	<<2 -6 -6 -2 -14 -15 -10 3 16 15]]	Bipelog	35.694	33/32 45/44 50/49
5	<<24 8 -8 24 -43 -80 -45 -41 28 95]]		37.220	385/384 441/440 9375/9317
6	<<10 2 2 6 -20 -25 -25 -1 7 10]]		39.151	50/49 121/120 176/175
7	<<4 4 4 -4 -3 -5 -20 -2 -23 -25]]		39.912	33/32 36/35 50/49
8	<<33 13 -11 31 -56 -110 -65 -62 27 125]]		40.785	385/384 441/440 234375/234256
9	<<6 -2 -2 10 -17 -20 -5 1 30 35]]		41.563	45/44 50/49 385/384
10	<<1 -3 -11 -1 -7 -20 -5 -17 8 35]]		42.049	33/32 45/44 126/125
11	<<13 9 1 19 -16 -35 -15 -23 13 50]]		43.336	126/125 176/175 864/847
12	<<8 8 8 8 -6 -10 -15 -4 -9 -5]]		43.387	36/35 50/49 121/120
13	<<15 3 -5 17 -30 -50 -25 -20 29 65]]		45.623	385/384 441/440 625/616
14	<<3 7 -1 -3 4 -10 -15 -22 -31 -5]]		46.385	33/32 36/35 352/343
15	<<5 1 9 11 -10 0 0 18 22 0]]		46.775	36/35 45/44 363/343
16	<<5 1 -7 -5 -10 -25 -25 -19 -15 10]]		46.970	33/32 126/125 176/175
17	<<5 1 -7 11 -10 -25 0 -19 22 55]]		48.038	45/44 126/125 385/384
18	<<3 7 -1 13 4 -10 10 -22 6 40]]		49.500	36/35 45/44 1029/1024

13-limit temperaments with badness below 0.04

Listed is the wedgie and the TE badness times 1000 for 32 temperaments with badness less than 0.04.

Rank	Wedgie	Name	Badness	Commas
1	<<1 -3 5 -1 3 -7 5 -5 1 20 8 18 -20 -10 14]]	Armodue	19.351	27/26 33/32 36/35 45/44
2	<<9 5 -3 7 11 -13 -30 -20 -16 -21 -1 7 30 42 12]]	Lupercalia	21.328	66/65 105/104 121/120 126/125
3	<<33 13 -11 31 19 -56 -110 -65 -92 -62 27 -4 125 94 -49]]		21.636	385/384 441/440 625/624 847/845
4	<<4 4 4 12 12 -3 -5 5 4 -2 14 13 20 19 -3]]		22.837	27/26 36/35 45/44 50/49
5	<<6 -2 -2 10 2 -17 -20 -5 -19 1 30 12 35 13 -30]]	Lemba	25.477	45/44 50/49 65/64 78/77
6	<<8 8 8 8 8 -6 -10 -15 -17 -4 -9 -11 -5 -7 -2]]		27.514	36/35 50/49 66/65 143/140
7	<<5 1 -7 -5 -1 -10 -25 -25 -20 -19 -15 -6 10 23 15]]		28.732	33/32 65/64 105/104 126/125
8	<<13 9 1 19 7 -16 -35 -15 -37 -23 13 -17 50 16 -46]]		28.920	78/77 126/125 144/143 176/175
9	<<24 8 -8 24 8 -43 -80 -45 -76 -41 28 -11 95 52 -61]]		29.407	169/168 385/384 441/440 625/624
10	<<2 -6 -6 -2 -10 -14 -15 -10 -23 3 16 -1 15 -6 -27]]		29.418	33/32 45/44 50/49 78/77
11	<<5 1 -7 11 -1 -10 -25 0 -20 -19 22 -6 55 23 -44]]		30.386	45/44 65/64 78/77 126/125
12	<<19 7 -1 13 9 -33 -55 -45 -56 -22 6 -5 40 29 -17]]		32.564	121/120 169/168 176/175 275/273
13	<<11 -1 -9 5 1 -27 -45 -30 -39 -18 15 6 45 36 -15]]		32.611	65/64 105/104 121/120 275/273
14	<<3 7 -1 13 9 4 -10 10 3 -22 6 -5 40 29 -17]]		32.664	27/26 36/35 45/44 507/500
15	<<18 10 -6 14 6 -26 -60 -40 -57 -42 -2 -23 60 39 -31]]		32.749	121/120 126/125 169/168 176/175
16	<<15 3 -5 17 13 -30 -50 -25 -35 -20 29 19 65 55 -18]]		33.081	105/104 144/143 275/273 625/616
17	<<7 11 3 9 5 1 -15 -10 -18 -24 -17 -29 15 3 -16]]		33.102	36/35 66/65 143/140 352/343
18	<<4 4 4 -4 -4 -3 -5 -20 -21 -2 -23 -24 -25 -26 1]]		33.195	33/32 36/35 50/49 65/64
19	<<22 14 -2 26 18 -29 -65 -35 -53 -44 12 -10 80 58 -34]]		33.792	126/125 144/143 176/175 847/845
20	<<4 4 4 12 -4 -3 -5 5 -21 -2 14 -24 20 -26 -58]]		33.951	36/35 45/44 50/49 65/64
21	<<1 -3 -11 -1 3 -7 -20 -5 1 -17 8 18 35 49 14]]		34.043	27/26 33/32 45/44 126/125
22	<<9 5 -3 7 -5 -13 -30 -20 -41 -21 -1 -30 30 -3 -43]]		34.114	65/64 78/77 121/120 126/125
23	<<10 2 2 6 -2 -20 -25 -25 -40 -1 7 -12 10 -13 -29]]		34.376	50/49 65/64 78/77 121/120
24	<<10 2 2 6 14 -20 -25 -25 -15 -1 7 25 10 32 26]]		35.284	50/49 66/65 105/104 121/120
25	<<6 -2 -2 -6 2 -17 -20 -30 -19 1 -7 12 -10 13 29]]		35.324	33/32 50/49 65/64 105/104
26	<<14 6 6 18 10 -23 -30 -20 -36 -3 21 1 30 6 -32]]		35.525	50/49 78/77 144/143 176/175
27	<<3 7 -1 -3 9 4 -10 -15 3 -22 -31 -5 -5 29 42]]		35.582	27/26 33/32 36/35 275/273
28	<<2 -6 -6 -2 6 -14 -15 -10 2 3 16 36 15 39 28]]		35.956	27/26 33/32 45/44 50/49
29	<<4 4 4 -4 12 -3 -5 -20 4 -2 -23 13 -25 19 56]]		36.915	27/26 33/32 36/35 50/49
30	<<1 -3 -11 -1 -13 -7 -20 -5 -24 -17 8 -19 35 4 -41]]		37.545	33/32 45/44 78/77 126/125
31	<<5 1 9 11 15 -10 0 0 5 18 22 31 0 9 11]]		38.328	27/26 36/35 45/44 363/343
32	<<5 1 9 11 -1 -10 0 0 -20 18 22 -6 0 -36 -44]]		38.808	36/35 45/44 65/64 275/273